Extending the residual income dynamics of Ohlson (1995): An analysis of the effects of net investments and industries.

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UNIVERSITY OF GRONINGEN

FACULTY OF ECONOMICS AND BUSINESS

MSc Finance

Extending the residual income dynamics of Ohlson (1995): An

analysis of the effects of net investments and industries.

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2 UNIVERSITY OF GRONINGEN

Extending the residual income dynamics of Ohlson (1995): An

analysis of the effects of net investments and industries.

Master’s thesis Finance Vincent van Iperen

S1980874 August 2016

Abstract

This research aims to assess the impact of net investments on the dynamics of residual income, as modelled in the famous residual income valuation model of Ohlson (1995). No literature previously assessed the impact of net investments on the persistence of residual income, the effect of industries on this persistence, nor presented industry-specific parameter estimations. Company data of 1144 firms over the years 1996-2015 is analyzed using a least-squares dummy variable approach. Scaled ‘last-year’s net investment’ is found to negatively affect next-year’s scaled residual income, suggesting a lag between the investment and the creation of residual income. Results provide compelling evidence that net investments and industry-specific parameters contribute to the residual income forecasting model’s accuracy, and thus add an interesting detail to the concept of the economic profit approach to valuation.

Keywords: Residual income, mean reversion, industry-effects, net investment JEL-code: G1, G3.

Word count: 11389

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1. Introduction

Two well-known valuation methods are the economic profit approach and the investment opportunity approach. Both aim to value companies based on the expected future residual income, but use distinct approaches to arrive at this value.

Central to this thesis is the question whether the economic profit approach could benefit from assumptions of the investment opportunity approach. Ohlson (1995) employs the economic profit approach, and innovatively models the residual income to express market value. His model and findings are widely cited, and serve here as the basis for this research.

The economic profit approach (EPA) discounts all future profits at a rate equal to the opportunity cost of capital to obtain economic profit (or, residual income). Added to the book value, this is what investors pay for a company’s stock. Ohlson (1995) models residual income as a modified autoregressive process, thereby using the mean-reverting property of residual income. The forecasting accuracy of residual income is vital for the practical applicability of the EPA.

The investment opportunity approach (IOA), introduced by Miller and Modigliani (1961), states the value of a company as the sum of its book value of assets, the residual income generated by its current assets, and the residual income that is created by potential future net investments. The IOA thus clearly distinguishes between current and future assets (net investments), thereby emphasizing the potential difference in the ability to create residual income of both ‘categories’ of operating assets.

With Ohlson’s (1995) residual income model as starting point, this research aims to answer a previously unanswered question: “How does ‘net investment’ affect residual income dynamics?”

Studies in the field of accounting and finance found a mean-reverting property of residual income over time (Freeman et al., 1982; Fama and French, 2000; Nissim and Penman, 2001). More than half a century ago already, the belief existed that returns above and returns below the mean rate of profitability will eventually converge due to competitive forces (Stigler, 1961). The convergence, or alternatively, the persistence of residual income is not only relevant for investors or managers that seek to maximize income. A wider understanding of competition and valuation is fueled by this thesis due to the broad assessment of residual income.

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5 investment variable, calculated as change in operating assets divided by the last year’s operating assets, is then added as predictor for next year’s scaled residual income. In addition to investigating the effect of net investment on residual income, I investigate whether industries have impact on the rate of convergence and the impact of net investments.

Results provide evidence that net investment significantly and negatively influences the next-year’s scaled residual income. Extending the residual income model with scaled net investment improves the explanatory power by approximately one percent, and the log-likelihood ratio test shows that the increased accuracy is significant.

Furthermore, there is evidence of a significant long-term residual income parameter, which indicates that residual income might not fully erode away. Industry-specific parameters are in some cases significantly different from other industries.

Miller and Modigliani’s (1961) assumption that residual income from an investment was generated immediately and into perpetuity is rejected in this thesis. The residual income persistence parameter of 0.83 shows that profitability slowly erodes away, and the coefficient on scaled net investments of approximately –0.10 indicates that an increase in invested capital not immediately increases profitability. However, Miller and Modigliani’s distinction between current capital and net investment certainly has potential to improve the EPA.

In addition, there is compelling evidence that in practice valuation can be enhanced by taking account of industry-effects. Practitioners often rely on ‘comparable companies’ and industry benchmarks to improve valuations or provide a sanity check. My results show that there are significant differences between industries, thus validate this practice.

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2. Theoretical background and hypothesis development

How does net investment affect the residual income valuation model of Ohlson (1995)? The purpose of this thesis is to answer that question.

When properly applied, two prevalent valuation approaches should yield the same results in perfect capital markets. The valuation approaches of interest are the economic profit approach, which is the basis of the Ohlson (1995) model, and the investment opportunity approach, which is introduced by Miller and Modigliani (1961). Despite the shared focus on residual income (used in Ohlson’s concepts but synonymous with economic profit) as value driver, the distinctive element of the investment opportunity approach is that it explicitly distinguishes between the value of the assets in place and the value of net investments in the future.

This distinction between the two sources of value might be conceptually more attractive when the return on assets in place differs from the return on net investments. Whether valuation would benefit from this distinction, is – broadly speaking – one of the questions I aim to answer.

The purpose of this thesis is to assess how net investment influences residual income dynamics as introduced by Ohlson (1995), and in turn affects company valuation. I assess the effects of net investment by including it as a variable in the residual income model of Ohlson (1995), and in turn measure and test whether and how the explanatory power and the parameters change.

Although several studies discuss the link between industries and company-performance, no papers present industry-specific parameter estimates used in Ohlson’s model. To the extent that the parameters differ per industry, this thesis aims to contribute to the theory and practice for professionals in the field of valuation.

This theory section first introduces the economic profit approach and the investment opportunity approach. Second, I elaborate on the residual income dynamics as introduced by Ohlson (1995). Third, I argue how favorable elements of the investment opportunity approach can enhance the residual income dynamics of Ohlson (1995). I document why and how industry-specific parameter estimation is innovative, useful, and could add to the collective understanding of residual income dynamics.

2.1. The economic profit approach

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7 discounted value of all future dividends. Using that assumption, Ohlson (1995) uses the clean surplus accounting relationship to arrive at his residual income valuation (RIV) model. The clean surplus accounting (CSA) relationship is used to algebraically rewrite dividends as a function of book value and earnings (equation (1)).

𝐵𝑉𝐸_𝑡 = 𝐵𝑉𝐸_𝑡−1+ 𝑁𝐼_𝑡− 𝑑_𝑡, (1)

Where 𝐵𝑉𝐸𝑡 is the book value of equity at year t, 𝑁𝐼_𝑡 is the net income of year t, and

𝑑_𝑡 is the dividends or net cash outflow at year t.

The EPA takes the opportunity cost of capital into account, thus reducing ‘profit’ by the required return on invested capital. All profit in excess of the required rate of return is called the residual income, and increases value. See equation (2).

𝑋𝑡 = 𝑁𝐼𝑡− 𝑘𝑡𝐸 × 𝐵𝑉𝐸𝑡−1, (2)

Where 𝑋_𝑡 is the residual income of year t, 𝑁𝐼𝑡 is the net income of year t,

𝑘𝑡𝐸 is the relevant discount rate reflecting the opportunity cost of capital, and 𝐵𝑉𝐸_𝑡−1 is the book value of equity at ending year t-1.

Now, residual income is specified and its link with value creation is established. The RIV builds on the hypothesis that value equals the sum of all discounted future dividends and the CSA relationship. The RIVM is explained in equation (3) below.

𝑉𝑎𝑙𝑢𝑒_𝑡𝑅𝐼𝑉𝑀 = 𝐵𝑉𝐸_𝑡+ ∑ 𝐸𝑡[𝑋𝑡+𝜏] (1 + 𝑘𝐸₎𝜏 ∞

𝜏=1

, (3)

Here, (market) value of equity is modelled as the current book value of equity plus the sum of all discounted future expected residual income.

𝐵𝑉𝐸𝑡 is the book value of equity at year t, 𝑋_𝑡+𝜏 is the residual income over year 𝑡 + 𝜏, and

𝑘_𝑖𝐸 is the discount rate, or required rate of return on equity.

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8 An advantageous property of the RIV model is that all required inputs can be derived from the income statement and balance sheet, thus no dividend forecasts are needed (Lo & Lys, 2000).

Before elaborating on the contributions of Ohlson (1995) to the RIVM, the contrasting investment opportunity approach is explained.

2.2. The investment opportunity approach

Miller and Modigliani (1961) present a model that explicitly factors in the value of growth. The value of a firm is split up in three components: a) the book value of the invested capital, b) the (market) value generated by the current invested capital (“assets in place”) and c) the (market) value generated by future net investments (“investment opportunities”). In symbols, see equation (4): 𝑉_𝑡𝑀𝑀 _{= 𝐴} 𝑡+ (𝑎𝑡+1− 𝑘) × 𝐴𝑡 𝑘 + ∑ 𝐼𝑡+𝑠 (1 + 𝑘)𝑠 ∞ 𝑠=1 ×𝑖𝑡+𝑠 − 𝑘 𝑘 , (4)

Where 𝐴𝑡 is the book value of invested capital in year t, 𝑎_𝑡 is the return on invested capital (assets) in year t,

𝐼_𝑡+𝑠 is the change in invested capital (𝐴_𝑡+𝑠− 𝐴_{𝑡+𝑠−1}) where s indicates each subsequent year

𝑖𝑡+𝑠 is the return on net investment in year t, 𝑘 is the opportunity costs of capital.

A clearly visible difference from the EPA is that the IOA distinguishes between the current assets in place and the (potential) value generated by net investments. Considering net investments as an option, managers are only likely to invest their available funds when return on investment (𝑖) exceeds the market rate of return (𝑘), which is the opportunity cost of capital. By assumption, each ‘growth opportunity’ where 𝑖 > 𝑘 will add to the value of the firm, immediately after investment and will do so into perpetuity. When return on net investments equals return on current assets (𝑖 = 𝑎), although unlikely, it appears less useful distinguish between both sources of value.

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9 vis-à-vis their rivals. Examples are patents and location advantages (Miller and Modigliani, 1961). Contrasting literature states that competition erodes profits, thereby showing a converging trend to a mean profit level (Brooks and Buckmaster, 1976; Freeman et al., 1982; Fama and French, 2000). This is in sharp contrast with the investment opportunity approach, where profits sustain forever. Despite this somewhat unrealistic assumption, the IOA is nevertheless attractive in the way it separates current from future profits.

2.3. Ohlson (1995): Residual income and information dynamics.

While the EPA and the IOA formed the basis for part of the valuation literature, a somewhat more recent interest in the EPA started after Ohlson (1995) introduced an innovative modification to the existing EPA to value equity of a company. Ohlson’s (1995) model is innovative due to the modelling of residual income, where he makes use of the mean-reverting property of residual income over time and an additional variable that captures value-relevant information not (yet) included in the current share price.

The market value of equity of a firm is expressed in terms of (1) book value, (b) a multiple of residual income and (c) a multiple of the information component:

𝑉_𝑡𝑂ℎ𝑙𝑠𝑜𝑛 = 𝐵𝑉𝐸_𝑡+ 𝛼₁𝑋_𝑡+ 𝛼₂𝜈_𝑡 (5) Where 𝐵𝑉𝐸_𝑡 is the book value of equity at year t,

𝑋_𝑡 is the residual income of year t,

𝜈𝑡 is the information component, which covers all value-relevant ‘other information’ not yet included in the financial statements and thus the residual income variable.

In Ohlson (1995), residual income and the ‘other information’ variable follow a modified autoregressive process.

𝑋_𝑡+1= 𝜔𝑋_𝑡+ 𝜈_𝑡+ 𝜖_1,𝑡+1, (6)

Where 𝜔 is the persistence parameter of residual income, and

𝜈_𝑡 is the variable containing ‘other information’, which is specified in equation (7), 𝜖_1,𝑡+1 is the zero-mean disturbance term with standard deviation one.

𝐸[𝜈_𝑡+1] = 𝜆𝜈𝑡+ 𝜖2,𝑡+1, (7)

Where 𝜆 is the persistence of the information variable, and

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10 In equation 6 and 7, the persistence parameters are assumed fixed and known, and are determined by the firm’s economic environment and accounting principles.

The persistence parameters (𝜔, 𝜆) are bound to be non-negative and smaller than one. The higher each parameter, the more sensitive the market value of equity is to changes in the respective variable (𝑅𝐼𝑡, 𝜈𝑡) (Ohlson, 1995). Hence, it is worthwhile for the improvement of company valuation to expand the knowledge about these parameters. Section 2.6 elaborates on the persistence of residual income.

‘Other information’ includes all value-relevant information that is not yet included in the accounting information. Researchers applying the Ohlson (1995) model often rely on analyst forecasts as a proxy for this variable. Other information could be of interest to fully understand residual income dynamics; however, the variable is not further defined, hence difficult to implement in this thesis. Therefore, ‘other information’ is omitted from this analysis.

2.4. Net investment

The purpose of this paper is to investigate the effect of net investment on the residual income forecasting ability of Ohlson’s (1995) ‘residual income dynamics’. His model of the behavior of residual income (economic profit) can be seen above in equation (6). Implied, by assumption, is that all relevant information regarding future residual income is included in the current level of residual income and the ‘information component’. Contrastingly, Miller and Modigliani (1961) distinguished between the current assets and net investments (growth opportunities). While the aims of Ohlson (1995) and Miller and Modigliani (1961) are alike, the latter have been able to articulate an intuitively appealing distinction that is still lacking in the Ohlson (1995) model.

Net investment in absolute value is positively linked to residual income in absolute value when profitability rate and the leverage ratio remain relatively constant (Liu and Ohlson, 2000; Myers, 2000). However, the effect of net investment on scaled residual income is not yet widely discussed in literature.

If the return on net investment is not equal to the return on current operating assets, residual income forecasting might in line with Modigliani and Miller benefit from including ‘net investment’ in the model. This is formulated into hypothesis 1:

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11 No upfront predictions regarding the coefficient of net investments can be made, but two rational expectations need to be mentioned:

If the return on net investments is higher than return on current invested capital (as in the IOA), the variable should provide a positive coefficient. Managers are, of course, expected to invest in value-increasing activities. However, there is a likely lag between the moment of investment and the (optimum) residual income creation that results in a first-year negative relationship.

Additionally, due to scaling by previous-year’s invested capital, the residual income is divided by a (recently) larger denominator, while the increase in residual income might not yet offset this effect.

Although opposing, either argument expects a relationship between net investment and residual income. This relationship is tested by means of hypothesis 2:

Hypothesis 2: residual income is influenced by previous-year’s net investments.

In section 3: ‘Methodology’, I document the empirical assessment of the above and following hypotheses.

2.5. Long-term residual income

As described above, Ohlson (1995) makes use of the predictability of the autoregressive process of residual income. By assumption, the returns eventually converge to zero. This assumption is too restrictive, since some firms are able to achieve long-term positive (or negative) residual income. When residual income always erodes to zero, market-to-book ratios should eventually become one. A look at the ratios of many firms shows that this is not a realistic assumption.

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12 Hypothesis 3: Long-term residual income is existent in the residual income forecasting model.

2.6. The persistence of residual income

The IOA assumes that assets generate profit at a level that persists into perpetuity. However, a large body of literature confirms the mean-reverting property of profits. Although no consensus has been achieved as to the ultimate reason for the convergence of profits, competitive forces are widely mentioned as influencing the rate of profit erosion (Stigler, 1961; Mueller, 1977; Mauboussin & Johnson, 1997; McGahan & Porter, 1999; Waring, 1996).

The persistence parameter of residual income (𝜔) is interpreted as proxy for competitiveness. The higher the persistence parameter, the slower profits converge. From an industry-wide perspective, supply and demand affect profitability. However, due to entry barriers, companies can protect themselves from new entrants (Porter, 1979) and thereby maintain favorable margins.

From the firm-level perspective, companies can be seen as a bundle of value-generating resources, called the resource-based view (RBV) (Barney, 1991). Distinctive firm-specific resources can create distinctive competitive advantage. E.g. ‘power over suppliers’ increases net operating profitability (Dickinson & Sommers, 2012). Companies can protect themselves from the forces of competition by applying the VRIN framework of Barney (1991) which states that persistent competitive advantage is the result of resources that are ‘valuable’, ‘rare’, ‘inimitable’ and ‘non-substitutable’. When many companies have unique and competitive resources, persistence is assumed to be higher. Therefore, the persistence parameter tells us something about competitiveness in the market.

Departing from the individual reasons for the rate of convergence, this research looks at the industry-wide level of persistence. In addition, profit margin and asset turnover have been found to converge to industry-level benchmarks (Soliman, 2004). Establishing the convergence (persistence rate below one; 𝜔 < 1) is required before proceeding with the rest of the empirical research.

Hypothesis 4: residual income converges toward a mean rate.

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13 explain a part of next-year’s profitability. A change in the persistence parameter would hint at a conceptual link between Miller & Modigliani (1961) and Ohlson (1995) regarding the forecasting of residual income. Whether the persistence parameter changes is tested by the following hypothesis:

Hypothesis 5: The persistence parameter of residual income changes when net investments are included in the residual income forecasting model.

2.7. Industry-specific parameter estimation

The focus in Ohlson (1995) has been on the valuation of a single company. Practitioners, however, often rely on information of comparable companies in the same industry for valuation purposes (Koller et al., 2010). The question arises to what extent the link between industries and company performance is important for valuation.

The effect of industries is not yet discussed in relation with the residual income approach or the model of Ohlson (1995). In other literature fields, there appears to be some evidence that industry-differences might exist in the residual income forecasting model of Ohlson (1995). If that is the case, then parameter estimates of interest in this research could be more accurate if made industry-specific.

The performance of firms is strongly determined by their industry, according to Schmalensee (1985). Gebhardt et al. (2001) find systematic interindustry differences in their estimation of cost of capital for companies. They assume convergence to industry-specific benchmarks. Industry-specific adjustments benefit forecasting changes in future operating profitability (Soliman, 2004). Accordingly, Fairfield et al. (2009) find that industry-specific models are better at predicting growth (growth in net operating assets, book value and sales).

Not all conclusions point at industry-level models being more accurate than economy-wide models. Obviously, companies’ environment is decomposable in multiple ways. Strategic groups within an industry have considerable influence on each other’s performance due to the ‘segmented’ competitiveness in such a group (Porter, 1979). Even some findings suggest that there is so much heterogeneity among firms that industry-level analyses are not better than at the economy-wide perspective (MacKay and Phillips, 2005).

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14 IOA and the EPA, and extends the knowledge on residual income dynamics. Also for practitioners, empirical results regarding the industry-specific parameters can be useful by enhancing their valuation methods. Industry-specific competition parameters (𝜔_𝑗, where subscript 𝑗 denotes the industry) can differ; hence indicate that competitiveness is in aggregate not equal across industries. This research aims to uncover whether that is the case in this particular valuation context. The following hypotheses aim to identify the above-mentioned effects on parameters and explanatory power:

Hypothesis 6: Industry-specific competition parameters have different values across industries.

Hypothesis 7: The effect of net investment on next-year’s residual income is different across industries.

Hypothesis 8: Residual income forecasting models with industry-specific parameters have higher explanatory power than when economy-wide parameters are used.

3. Methodology

In this section, I provide an overview of the models, as far as they have not been discussed in the previous section. Second, I document the variables used in the estimation. Third, I elaborate about the sample composition. Fourth, I document and motivate how the hypotheses are tested.

3.1. Modeling the relationship between net investments and residual income

Testing the hypothesized effects is done using two residual income models. Both models originate from the work of Ohlson (1995). More specifically, they are based on the specification of the stochastic process of ‘residual income’ as described in assumption A3 (Ohlson, 1995: pp 668). Model (1) is the benchmark model, rather similar to the autoregressive model of residual income. Model (2) applies the ‘net investment’ restriction. See equations (10) and (11).

A small difference between Ohlson’s specification and the current, is that Ohlson (1995) models the ‘future’ residual income. In this thesis, the empirical analysis focuses on historical data and thus 𝑥_𝑖𝑡 is estimated instead of 𝑥_𝑖𝑡+1. The concept remains the same, but the specification better aligns with the calculation of the dataset.

Residual income is forecasted using the equation below:

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15 Where 𝑋 represents residual income (dollar value) of firm 𝑖 in year 𝑡,

𝐴 is the invested capital (dollar value),

I is the net investment (dollar value) variable (𝐴_𝑖𝑡−1− 𝐴_𝑖𝑡−2), 𝛼 denotes the parameter for long-term residual income, for industry 𝑗, 𝜔 denotes the persistence parameter for residual income

𝛾 denotes the net investment parameter,

𝜖 represents the zero mean, standard deviation one disturbance term.

Due to the empirical problems inherent with dollar values, the variables are scaled. As taking logarithms of negative values is impossible, it is appropriate to scale each variable by the past-year’s value of invested capital. Doing so, the variable set consists of ratios. In section 3.2 I document the variable construction procedure. Scaling 𝐴_𝑖𝑡−2 by itself leaves us with 𝛼_𝑗 as equivalent of a constant. This is in line with the suggestion of Lo & Lys (2000) that adding a constant to the model is an appropriate solution to account for long-term (non-zero) residual income. Scaling occurs as follows in equation (9):

𝑋𝑖𝑡 𝐴_𝑖𝑡−2 = 𝛼𝑗 × +𝜔𝑗× 𝑋𝑖𝑡−1 𝐴_𝑖𝑡−2+ 𝛾𝑗× 𝐼𝑖𝑡−1 𝐴_𝑖𝑡−2+ 𝜖𝑖𝑡, (9)

Now I arrive at the benchmark model in equation (10):

𝑥_𝑖𝑡 = 𝛼_𝑗 + 𝜔_𝑗𝑥_𝑖𝑡−1+ 𝜖_1,𝑖𝑡, (10)

Where 𝑥 represents the scaled residual income of company 𝑖 at year 𝑡, Constant 𝛼_𝑗 represents the long-term residual income,

𝜔_𝑗 represents the persistence parameter of scaled residual income,

𝜖_1,𝑖𝑡 represents the mean zero, standard deviation of one disturbance term.

The extended model, model (2), applies a restriction on the added ‘net investment’ variable. Net investment is scaled by the previous year’s level of invested capital and included as follows in equation (11):

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16 𝑖_𝑖𝑡−1 is scaled net investment of firm 𝑖 in year 𝑡,

Constant 𝛼𝑗 represents the long-term residual income of industry 𝑗, 𝜔𝑗 represents the persistence parameter of scaled residual income,

𝛾_𝑗 denotes the parameter of the effect of net investment on residual income, 𝜖_2,𝑖𝑡 denotes the mean zero, standard deviation of one disturbance term.

The addition of 𝑖_𝑖𝑡−1 provides insights in the dynamics of residual income. The hypotheses are centered around this restriction, and multiple tests can be done regarding the changes and improvements of model (2) compared to model (1).

Several modelling choices need some clarification. The net investment variable is chosen to represent one year’s change in net investment. Many other specifications could be tested, but as a starting point, the one-year net investment seems appropriate to distinguish the current invested capital from ‘future’ invested capital.

The autoregressive component 𝜔_𝑗 (although slightly modified due to the scaling transformation of 𝑋_𝑖𝑡 versus 𝑋_𝑖𝑡−1, both divided by 𝐴_𝑖𝑡−1), is tested before in a comparable fashion. Dechow et al. (1999) show that only the first-order lagged variable is sufficient to capture the persistence effects. Therefore, I apply only the simple one-year lag to model (1) and (2). Persistence parameter 𝜔_𝑗 is assumed to have a value of 0 ≤ 𝜔_𝑗 < 1.

Net investment parameter 𝛾𝑗 is assumed to have a value in the range of (−1 < 𝛾𝑗 < 1). Feltham and Ohlson (1995) include the expected growth rate of book value in their extended residual income model, however only indirectly and with a fixed parameter.

The models described above provide the concept of my empirical assessment. The procedure of estimation and testing the hypotheses is documented in section 3.4. Before that, I discuss the data set and sample composition.

3.2. Data collection and variable construction

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17 Table 1: Collected raw data

Symbol Variable name Datastream code Remarks 𝐸𝐵𝐼𝑇_𝑖𝑡 Earnings before interest and taxes

WC18191 Represents earnings of firm i, in year t, before interest and taxes have been deducted.

𝑇𝐸_𝑖𝑡 Income tax expense

WC01451 Represents all income taxes on the income of a company by federal, state and foreign governments 𝐵𝑉𝐸_𝑖𝑡 Book value

of equity

WC03995 Equals total assets minus total liabilities

𝑀𝑉𝐸_𝑖𝑡 Market value of equity

MV Equals share price × number of ordinary shares

𝑇𝐷_𝑖𝑡 Total debt WC03255 Includes all long and short term debt, and includes also interest bearing capitalized lease obligations 𝑅𝐼𝑀,𝑡 Total return

index of the market

RI Monthly total return index of the ‘MSCI all 2500 investable US firms’ (index MSUEI25) over the years 1991-2015. Adjusted for dividends and stock splits.

𝑅𝐼𝑖,𝑡 Total return index of firms

WC01251 Monthly total return index of each firm 1991-2015, when available

𝐼𝐸_𝑖𝑡 Interest expense

WC01251 Equals interest expense on long and short term debt, capitalized lease obligations and amortization expenses associated with the issuance of debt. 𝐶_𝑖𝑡 Cash WC02001 Represents cash and short term investments

I construct the variables from the models by using raw data available from the Reuters Datastream database.

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18 here ‘invested capital’ exclude cash and short term investments, which are considered non-operating assets.

This research measures residual income by ‘excess operating profit’, which is operating profit deducted by the required rate of return times invested capital. The operating profit represents value creation from operating assets and is calculated by subtracting the effective tax rate from EBIT (Koller et al., 2010). I calculate the effective tax rate by taking the median of the ratio of reported tax expenses divided by earnings before taxes (EBT). The median effective tax rate is taken per industry group.

The required rate of return (cost of capital) is calculated using the weighted average cost of capital method, which combines the debt and equity risk into one company-specific risk measure. Since companies within the same industry show similar characteristics regarding operating risk, optimal leverage ratio and industry-related developments such as growth, I construct an industry-specific and time-invariant cost of capital (Koller et al., 2010).

Weights of debt and equity are based on the industry median leverage ratio (𝑤_𝑗𝐷). Cost of debt comes from synthetic ratings. Damodaran (2016) provides credit spreads related to interest coverage ratios. To facilitate industry-specific cost of capital calculation, median interest coverage ratios per industry are used. To include the benefits of the so-called tax shield, cost of debt is for all industries reduced by the 35% marginal statutory U.S. tax rate (OECD, 2016). The cost of equity capital is calculated by the capital asset pricing model (CAPM).

The market-required return on equity capital following the CAPM is the risk-free rate plus the market risk premium (MRP) multiplied by a factor for firm risk, the beta. The risk-free rate is assumed time-invariant at a level of 2.5%. The actual risk-free rate changes over time, and fluctuates over the past 20 years between 0% and 4% approximately. According to Koller et al. (2010), a market risk premium of 5% is appropriate.

The beta is calculated by regressing each company’s monthly return index against the market return index, in this case the MSCI total return index of the 2500 largest investable US firms. The regression slope is the levered company beta. Each beta is unlevered using individual company-average leverage ratios, obtained with market value of equity and book value of debt as beta is the volatility relative to a market benchmark. Per industry, the median is taken of the companies’ unlevered betas, and re-leveraged using the industry-specific median of firm leverage ratios. As visible in table 3, the re-leveraged beta is 1.01 thus in line with theory.

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19 Table 2: Generated variables overview and calculation method

Symbol Variable name Calculation

𝑃_𝑖𝑡 Operating income 𝐸𝐵𝐼𝑇_𝑖𝑡× (1 − 𝑇_𝑗𝐸) 𝐸𝐵𝑇𝑖𝑡 Earnings before taxes 𝐸𝐵𝐼𝑇𝑖𝑡− 𝐼𝐸𝑖𝑡

𝑇_𝑗𝐸 Effective tax rate _{Median per industry of all (}𝑇𝐸𝑖𝑡

𝐸𝐵𝑇𝑖𝑡)

𝐴𝑖𝑡 Invested capital 𝑇𝐷𝑖𝑡 + 𝐵𝑉𝐸𝑖𝑡− 𝐶𝑖𝑡 𝑋_𝑖𝑡 Residual income (from

operations)

𝑃𝑖𝑡− (𝑘𝑗× 𝐴𝑖𝑡−1)

𝐼_𝑖𝑡 Net investment 𝐴_𝑖𝑡 − 𝐴_𝑖𝑡−1 𝑥_𝑖𝑡 Scaled residual income 𝑋_𝑖𝑡/𝐴_𝑖𝑡−2 𝑥𝑖𝑡−1 Scaled last-year’s residual

income

𝑋𝑖𝑡−1/𝐴𝑖𝑡−2

𝑖𝑖𝑡 Scaled net investment 𝐼𝑖𝑡−1/𝐴𝑖𝑡−2 𝑘_𝑗 Cost of capital, industry

median

𝑤_𝑗𝐷 × 𝑘_𝑗𝐷× (1 − 𝑇_𝑗𝑀) + 𝑤_𝑗𝐸× 𝑘_𝑗𝐸

𝑤_𝑗𝐷 Weight of debt, industry median, market value (MV)

Median per industry of all ( 𝑇𝐷𝑖𝑡

𝑇𝐷𝑖𝑡+𝑀𝑉𝐸𝑖𝑡)

𝑤_𝑗𝐸 Weight of equity 1 − 𝑤_𝑗𝐷)

𝑘_𝑗𝐷 Cost of debt 𝑟𝑓 + 𝐶𝑆𝑃𝑗

𝐶𝑆𝑃_𝑗 Credit spread Matching industry median of 𝐼𝐶𝑅𝑖𝑡 with debt spreads as implied by the market (Damodaran, 2011)

𝐼𝐶𝑅_𝑖𝑡 Interest coverage ratio 𝐸𝐵𝐼𝑇_𝑖𝑡/𝐼𝐸_𝑖𝑡

𝑘_𝑗𝐸 Cost of equity 𝑟𝑓 + 𝛽_𝑗× 𝑀𝑅𝑃

𝛽_𝑗 Leveraged industry beta

(𝛽_𝑢𝑗) × [1 + 𝑀𝑒𝑑𝑖𝑎𝑛_𝑗(𝑇𝐷𝑖𝑡

𝑀𝑉𝐸𝑖𝑡)_𝑗]

𝛽_𝑢𝑗 Unleveraged beta, industry median

𝑀𝑒𝑑𝑖𝑎𝑛(𝛽_𝑢𝑖𝑡)_𝑗

𝛽_𝑢𝑖𝑡 Firm unleveraged beta _𝛽

𝑙𝑖𝑡/ [1 + ( 𝑇𝐷𝑖𝑡

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20 𝛽_𝑙𝑖𝑡 Firm leveraged beta 𝜎𝑅𝑚,𝑅𝑖

𝜎_𝑅𝑚2 , where 𝑅𝑚 and 𝑅𝑖 are monthly returns of the MSUEI25 and companies, respectively, estimated over the complete sample period

The variable construction is for a large part done with median values (overall and per industry). To provide an overview, table 3 displays the inputs I used for the cost of capital (WACC). For each industry, the median value is given when company-subscript 𝑖 is added; the industry-subscript 𝑗 is attached when industry-specific variables are constructed using the other inputs.

Table 3: Cost of capital construction inputs

Industry name 𝑆𝐼𝐶 𝛽_𝑖𝑙𝑒𝑣 𝛽_𝑖𝑢𝑛𝑙𝑒𝑣 (

𝑇𝐷

𝑀𝑉𝐸)_𝑗 𝛽_𝑗𝑙𝑒𝑣 𝑘_𝑗𝐸

Mining 10 1.044 0.696 0.375 0.957 0.073

Manufacturing - Natural products 20 0.755 0.593 0.302 0.771 0.064 Manufacturing - Chemical products 28 1.113 0.855 0.149 0.983 0.074 Manufacturing - Machinery and equipment 35 1.274 1.071 0.112 1.191 0.085 Transportation, Communications, Electric,

Gas and Sanitary service 40 0.807 0.388 0.823 0.707 0.060 Wholesale and retail trade 50 1.071 0.862 0.181 1.018 0.076

Services 70 1.250 1.012 0.132 1.145 0.082

Complete sample 1.112 0.844 0.204 1.016 0.076

Table 3: Cost of capital construction inputs, cont’d

Industry name _{𝑆𝐼𝐶 𝐼𝐶𝑅}

𝑗 𝐶𝑆𝑃𝑗 𝑘𝑗𝐷 𝑤𝑗𝐷 𝑇𝑗 𝐸𝑓𝑓

𝑘_𝑗

Mining 10 5.386 0.018 0.043 0.273 0.357 0.061

Manufacturing - Natural products 20 6.461 0.013 0.038 0.232 0.355 0.054 Manufacturing - Chemical products 28 4.386 0.023 0.048 0.130 0.263 0.069 Manufacturing - Machinery and equipment 35 7.899 0.011 0.036 0.101 0.277 0.078 Transportation, Communications, Electric,

Gas and Sanitary service 40 3.235 0.043 0.068 0.452 0.364 0.053 Wholesale and retail trade 50 9.379 0.011 0.036 0.153 0.370 0.068

Services 70 6.260 0.013 0.038 0.116 0.329 0.076

Complete sample 5.671 0.018 0.043 0.169 0.330 0.068

Note: 𝑆𝐼𝐶 denotes the industry code. 𝛽𝑖𝑙𝑒𝑣represents the median time-invariant company beta, 𝛽𝑖𝑢𝑛𝑙𝑒𝑣 is

the company beta, unlevered using the annual leverage ratios, (𝑇𝐷

𝑀𝑉𝐸)_𝑗is the median leverage ratio per

industry, 𝛽𝑗𝑙𝑒𝑣 is the beta, relevered using median industry leverage ratios. 𝑘𝑗𝐸 is the cost of equity capital

calculated per industry, 𝐼𝐶𝑅𝑗is the interest coverage ratio, 𝐶𝑆𝑃𝑗 is the synthetic credit spread derived

from Damodan (2016) online, 𝑘𝑗𝐷 is the cost of debt, 𝑤𝑗𝐷 is the industry-median weight of debt, 𝑇𝑗 𝐸𝑓𝑓

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21 3.3. Sample composition

The sample consists of 1144 in the United States listed companies. On average, 15.7 yearly observations per company yield a total of 17,923 company-year observations. All companies in the financial and public services industries are excluded, as their competitive environment and internal structure are fundamentally different from the rest of the sample. In addition, firms with missing SIC-codes are excluded from the sample.

SIC, which stands for Standard Industrial Classification, is a system to categorize firms by a code of four digits. I categorize firms in seven industry groups in accordance with the SIC system, to maintain sufficiently large sub-samples. The regression variables for the complete sample and each industry group are summarized in two tables. In table 4: ‘Correlation matrix of key variables in the complete sample’, I document the Pearson correlation between the dependent and independent variables. In appendix Table A3: ‘Correlation matrices per industry’, the correlation matrices of each industry can be found. In table 5, I present the descriptive statistics of the (industry-specific) variables as used in the regression. See Appendix Table A1: ‘Overview of industry groups’ for a complete description of each industry group’s activities.

Table 4: Correlation matrix of key variables in the complete sample Complete sample

𝑥𝑖𝑡 𝑥𝑖𝑡−1 𝑖𝑖𝑡−1

𝑥_𝑖𝑡 1

𝑥𝑖𝑡−1 0.7690 1

𝑖_𝑖𝑡−1 0.0245 0.1550 1

Note: the correlations are the Pearson product-moment correlations. The dependent variable 𝑥𝑖𝑡 is the

scaled residual income, 𝑥𝑖𝑡−1 is the scaled last-year’s residual income and 𝑖𝑖𝑡−1 is the scaled net

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22 Table 5: Descriptive statistics of industry-specific variables

Variable: Scaled current year's residual income (𝑥𝑖𝑡)

SIC-code Mean Median St. Dev. Min Max Obs.

10 0.0635 0.0483 0.2843 -1.7668 1.9902 1008 20 0.0971 0.0573 0.2559 -1.7668 1.9902 1528 28 0.1000 0.0713 0.9022 -1.7668 1.9902 3059 35 0.0328 0.0499 0.5296 -1.7668 1.9902 4880 40 0.0445 0.0218 0.2564 -1.7668 1.9902 2472 50 0.0969 0.0720 0.3363 -1.7668 1.9902 2544 70 0.1346 0.0463 0.6607 -1.7668 1.9902 2662 All 0.0768 0.0495 0.5591 -1.7668 1.9902 18153

Variable: Scaled previous year's residual income (𝑥_𝑖𝑡−1)

10 0.0677 0.0492 0.2346 -1.4276 1.7510 1007 20 0.0850 0.0541 0.2189 -1.4276 1.7510 1535 28 0.1042 0.0695 0.7663 -1.4276 1.7510 3057 35 0.0382 0.0514 0.4524 -1.4276 1.7510 4880 40 0.0390 0.0218 0.2201 -1.4276 1.7510 2475 50 0.0838 0.0663 0.2887 -1.4276 1.7510 2561 70 0.1183 0.0417 0.5708 -1.4276 1.7510 2659 All 0.0732 0.0475 0.4772 -1.4276 1.7510 18174

Variable: scaled previous year's net investments (𝑖_𝑖𝑡−1)

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23 3.4. Estimation and testing methodology

The hypotheses are tested after the two models are estimated. Estimation is conducted via the well-known ordinary least-squares method (OLS). However, due to the information contained in each specific company, and the time-series behavior of residual income, the fixed-effects estimation method is applied. Both models’ dependent variable is estimated using entity-dummies for the independent variables.

Residual income of that companies exhibit ‘fixed’ unique differences that might be visible in the dataset (e.g. the firm-specific level of scaled residual income) is confirmed by the Hausman test. In section 4, ‘Results’, I document the results of the Hausman test. Year-effects are in this research not taken into account, but could arguably be covered in future research.

Industry-effects are tested for by including dummy variables for each of the seven industries. Since separate industry-dummies are omitted in fixed-effects estimation, I multiply each industry-dummy (1 or 0) with the (in)dependent variables.

Standard econometrical issues in financial research include heteroscedasticity, non-normality and autocorrelation. In this dataset, heteroskedasticity and autocorrelation are present. The modified Wald-test for group wise heteroskedasticity shows a p-value of 0.000, confirming heteroskedasticity. The Woolridge test for autocorrelation in panel data provides a p-value of 0.09 (Woolridge, 2002). Non-normality tends to be irrelevant for the validity of the results if the dataset is sufficiently large, which is the case.

In the regression results, I take account of these issues by adjusting the standard errors. Regression coefficients are reported with the Driscoll-Kraay standard errors. These standard errors prevent from falsely rejecting the null-hypothesis, hence makes the results more conservative. Driscoll-Kraay standard errors account for heteroskedasticity, autocorrelation and possible correlation between companies. The econometrical software (Stata) is not capable of combining the Driscoll-Kraay standard errors with tests that involve comparing equality of parameters or comparing goodness-of-fit statistics of the models. As alternative, the software is able to compute Huber-White’s sandwich errors, that adjust for small non-normality issues such as heteroskedasticity and autocorrelation.

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24 Ultimately, the empirical analysis should answer the research question “How does ‘net investment’ affect residual income dynamics?”. In the literature framework I present eight hypotheses that facilitate this research in answering the central question.

First and foremost, I compare two models. The extended model (2) is compared with the benchmark model (1) on the ability to explain next-year’s scaled residual income. Both models are estimated with and without industry-specific parameters as seen in hypotheses 1 and 8. Adjusted R-squared and the likelihood ratio are used to compare the ‘fit’ of the model on the current dataset. If the adjusted R-squared of model (2) is higher than the adjusted R-squared of model (1), it means that the inclusion of scaled net investments is beneficial to the model. Adjusted R-squared is ratio of explained variance to total variance in the dependent variable, but ‘penalizes’ for complexity as a result of more variables. The likelihood ratio compares the fit of two models, and provides a p-value to determine which model is a better fit.

Secondly, the persistence parameter is tested for being equal to one, to confirm previous findings that residual income converges over time. Similarly, the coefficient of ‘scaled net investments’ and the constant are presented and tested against being zero. 95% confidence levels are applied throughout all tests. The coefficient tests to assess hypotheses 2, 3 and 4 are done using the Wald test.

Thirdly, the industry-effects in hypotheses 6 and 7 on respectively the persistence parameter and coefficient on net investment are tested. The Wald test is used to test whether equality of the coefficients should be rejected. An important remark should be made. The industry-specific coefficients can be estimated due to the multiplication of dummies with the independent variables. However, the constant could not differ in the fixed effects since time-invariant parameters are omitted in this procedure. Therefore, the long-term residual income is estimated on only the economy-wide level. For future research, this is an issue that could be investigated more in-depth.

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25

4. Results

Fixed effects panel data regression provides estimation results to test the hypotheses. Table 6: ‘Estimation results of the economy-wide models’ provides an overview of the parameters for the benchmark model (1) and the extended model (2). The extended model includes an extra restriction, which is the variable ‘net investments’. The estimation equation of model (1) is 𝑥_𝑖𝑡 = 𝛼 + 𝜔𝑥_𝑖𝑡−1+ 𝜖_𝑖𝑡, and the estimation equation of model (2) is 𝑥_𝑖𝑡 = 𝛼 + 𝜔𝑥_𝑖𝑡−1+ 𝛾𝑖_𝑖𝑡−1+ 𝜖_𝑖𝑡. In the first instance, industry-effects are ignored and the parameter subscript is dropped, disregarded. Hence, effectively four different equations are estimated.

The fixed effects approach rather than random effects is justified, since the Hausman test provides a p-value of 0.0008 (𝜒2 of 11.21) for model (1) and a p-value of 0.0037 (𝜒2 of 11.19) for model (2). In line with the reasoning in section 3.4 ‘estimation and testing methodology’, the fixed effects (within estimation) is applied.

Table 6: Estimation results of the economy-wide models

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Variables Benchmark model Extended model

Persistence parameter (𝜔) 0.825*** 0.848*** (0.006) (0.006) Investment parameter (𝛾) -0.099*** (0.005) Constant (𝛼) 0.018*** 0.033*** (0.003) (0.003) Observations 17,923 17,923 R-squared 0.627 0.636 Adj. R-squared 0.602 0.611 F-test 2081.46 1127.62 RMSE 0.350 0.346 Log-likelihood -6006 -5801

Note: Model (1) is estimated following 𝑥𝑖𝑡 = 𝛼 + 𝜔𝑥𝑖𝑡−1+ 𝜖𝑖𝑡 and model (2) is estimated using 𝑥𝑖𝑡 =

𝛼 + 𝜔𝑥𝑖𝑡−1+ 𝛾𝑖𝑖𝑡−1+ 𝜖𝑖𝑡. SIC-codes correspond to the industry groups, and are discussed in

appendix A1. RMSE is root mean-squared error and an alternative to the R-squared measure of explanatory power. Estimated with Driscoll-Kraay standard errors. Standard errors in parentheses (*** p<0.01, ** p<0.05, * p<0.1).

4.1. Results on the economy-wide model

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26 Both are tested against the null of hypothesis 4: 𝜔 = 1. P-values of 0.000 show that the persistence parameters are both significantly different from 1 and hence confirm the converging property of residual income as initially reported by e.g. Freeman et al., (1982) and Fama & French (2000). The persistence parameter is higher than the one estimated in Dechow et al., (1999), which is 0.62. Possible explanations might be that Dechow et al., (1999) perform their research at the equity level and have a fixed cost of equity of 12%, hence have a rather different level of analysis.

Of central interest is the variable ‘scaled net investment’. The investment coefficient (𝛾) turns out to be negative (– 0.099) and highly significant (p-value of 0.000). This implies that the relation between scaled net investment and next-year’s scaled residual income is negative. Two possible explanations appear most reasonable. First, simple mathematics show that a large increase in invested capital leads to a larger denominator in the scaling of residual income, resulting in an inherent decrease in the dependent variable. Second, net investments may exhibit a lag between the moment of investment and the moment it is optimally generating value. For example, capital could take a year to become fully efficient, after which some period of high ROIC and a subsequent decline in profitability follow. Future research could investigate the behavior of net investments in greater detail. These results show that the assumption of Miller and Modigliani (1961) where profits are generated immediately and forever after investment, should be abandoned in this residual income model.

By adding a constant (𝛼), I find evidence of long-term scaled residual income. The coefficients of model (1) and model (2), respectively 0.018 and 0.033 (both significant at the 0.01 level), reject the null hypothesis that the mean scaled residual income is equal to zero. This can imply that companies can have long-term residual income (monopoly rents) and we should reject the assumption of perfect competition is the models. An alternative clarification is that conservative accounting leads to positively biased scaled residual income (Lo and Lys, 2000).

4.2. Results on the industry-specific model

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27 the investment parameter, provides evidence that industries influence residual income dynamics, and potentially enhance the residual income forecasting model of Ohlson (1995).

Table 7: Estimation results of the industry-specific models

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Variables Benchmark model Extended model

𝜔_{𝑆𝐼𝐶10} 0.244* 0.269** (0.120) (0.119) 𝜔𝑆𝐼𝐶20 0.796*** 0.822*** (0.084) (0.083) 𝜔_{𝑆𝐼𝐶28} 0.909*** 0.918*** (0.049) (0.048) 𝜔_{𝑆𝐼𝐶35} 0.730*** 0.760*** (0.064) (0.060) 𝜔_{𝑆𝐼𝐶40} 0.728*** 0.738*** (0.083) (0.088) 𝜔_{𝑆𝐼𝐶50} 0.736*** 0.765*** (0.067) (0.067) 𝜔𝑆𝐼𝐶70 0.829*** 0.861*** (0.036) (0.030) 𝛾𝑆𝐼𝐶10 -0.043 (0.042) 𝛾_{𝑆𝐼𝐶20} -0.039** (0.015) 𝛾_{𝑆𝐼𝐶28} -0.052** (0.023) 𝛾_{𝑆𝐼𝐶35} -0.141*** (0.032) 𝛾_{𝑆𝐼𝐶40} -0.030 (0.030) 𝛾𝑆𝐼𝐶50 -0.080** (0.029) 𝛾_{𝑆𝐼𝐶70} -0.146*** (0.028) Constant (𝛼𝐴𝐿𝐿) 0.021** 0.035*** (0.008) (0.006) Observations 17,923 17,923 R-squared 0.633 0.643 Adj. R-squared 0.608 0.618 F-test 319.49 181.60 RMSE 0.347 0.342 Log-likelihood -5859 -5617

Note: Model (1) is estimated following 𝑥𝑖𝑡 = 𝛼 + 𝜔𝑗𝑥𝑖𝑡−1+ 𝜖𝑖𝑡 and model (2) is estimated using

𝑥𝑖𝑡 = 𝛼 + 𝜔𝑗𝑥𝑖𝑡−1+ 𝛾𝑗𝑖𝑖𝑡−1+ 𝜖𝑖𝑡. SIC-codes correspond to the industry groups, and are discussed in

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28 Table 7: ‘Estimation results of the industry-specific models’ shows the parameter estimates. In the industry-specific versions of the benchmark model and the extended model, 21 parameter comparisons per independent variable can be tested for equality (0.05 significance level). Persistence parameters are significantly different in 7 out of 21 industry combinations (11 of 21 with 90% confidence). Net investment parameters differ significantly in 5 of the 21 industry combinations (9 of 21 with 90% confidence).

In addition, the scaled residual income (𝑥_𝑖𝑡−1) mean values per industry are in 18 out of 21 tests significantly different from other industries. These statistics are in itself sufficient evidence to conclude that industry-level estimates potentially improve the model as parameters can differ between industries. Results on the goodness-of-fit are documented in section 4.3.

How does including ‘net investment’ affect the persistence parameter in the model? Hypothesis 5 is tested using the likelihood ratio test available in Stata. After extending the residual income model with the scaled net investment variable, every persistence parameter shows an increased estimate. Coefficient tests across the two versions of the benchmark and extended model provide a chi-squared test statistic and a p-value. Results show that the economy-wide persistence parameter increases significantly after adding net investment. The industry-specific persistence parameters increase significantly (p-values < 0.05) except for the industry groups ‘Mining’ and ‘Transportation, communications, electric, gas and sanitary service’. See Table 8 below for the test results on the increase in persistence parameters.

Table 8: Persistence parameter increase due to net investment inclusion

Parameter comparison 𝜒2 − 𝑡𝑒𝑠𝑡 p-value

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29

Note: The benchmark model and the extended model persistence parameters are estimated, then tested for equality (𝐻𝑛𝑢𝑙𝑙: 𝜔 = 𝜔′) where the prime indicates the persistence parameter in the models with the scaled net investment variable. Model estimation is done with Huber-White robust standard errors.

4.3. Results on the comparison between the models’ goodness-of-fit

Hypotheses 1 and 9 require formal tests to accept or reject the null-hypotheses that the goodness-of-fit of the extended model (2) is equal to that of the benchmark model (1). For the goodness-of-fit measures, I provide two statistics: the adjusted R-squared and the log-likelihood ratio. By adding scaled net investments, adjusted R-squared increases from 60.2% to 61.1% when ignoring industry-effects, and increases from 60.8% to 61.8% when industry-specific variables are used.

A formal test statistic is provided with the likelihood ratio test. This test has a chi-squared distribution and comes with a p-value. At the 99% confidence interval, the extended models have a significantly better fit with the data than the benchmark models. Also, both the benchmark and extended model with industry-specific parameters have a significantly better fit than the economy-wide specifications. Thus, both the inclusion of ‘scaled net investments’ and the industry-specific parameters lead to a higher explanatory value. See table 9: likelihood ratio tests.

Table 9: Likelihood ratio comparisons between the models Likelihood ratio tests for the inclusion of net investments

LR-test ‘Nested’ model ‘Extended’ model 𝜒2-test p-value 1 𝑥𝑖𝑡 = 𝛼 + 𝜔𝑥𝑖𝑡−1+ 𝜖𝑖𝑡 𝑥𝑖𝑡 = 𝛼 + 𝜔𝑥𝑖𝑡−1+ 𝛾𝑖𝑖𝑡−1+ 𝜖𝑖𝑡 410.66 0.000 2 𝑥𝑖𝑡 = 𝛼 + 𝜔𝑗𝑥𝑖𝑡−1+ 𝜖𝑖𝑡 𝑥𝑖𝑡 = 𝛼 + 𝜔𝑗𝑥𝑖𝑡−1+ 𝛾𝑗𝑖𝑖𝑡−1+ 𝜖𝑖𝑡 485.00 0.000

Likelihood ratio tests for the effect of industry-specific parameters

LR-test ‘Nested’ model ‘Extended’ model 𝜒2_{-test p-value} 3 𝑥𝑖𝑡 = 𝛼 + 𝜔𝑥𝑖𝑡−1+ 𝜖𝑖𝑡 𝑥𝑖𝑡 = 𝛼 + 𝜔𝑗𝑥𝑖𝑡−1+ 𝜖𝑖𝑡 294.00 0.000 4 𝑥𝑖𝑡 = 𝛼 + 𝜔𝑥𝑖𝑡−1+ 𝛾𝑖𝑖𝑡−1+ 𝜖𝑖𝑡 𝑥𝑖𝑡 = 𝛼 + 𝜔𝑗𝑥𝑖𝑡−1+ 𝛾𝑗𝑖𝑖𝑡−1+ 𝜖𝑖𝑡 368.34 0.000

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30

5. Discussion and conclusion

The analysis on the residual income dynamics of Ohlson (1995) presents convincing evidence that the Economic Profit Approach (EPA) has potential to become more comprehensive and accurate when the residual income forecasting model includes ‘net investment’ as predictor.

The analysis focuses on the link between the net investments and residual income. Miller and Modigliani’s (1961) distinction between value from growth opportunities (resulting from net investments) and value from existing invested capital could benefit the EPA.

Based on the assumption that residual income from net investments is not equal to residual income of existing invested capital, I analyzed the effect of this distinction on the residual income model of Ohlson (1995).

Adding the variable ‘scaled net investment’ to the residual income model has two effects. Firstly, the persistence parameter increases. This increase might be a confirmation that the profitability of net investments in aggregate is distinct from the profitability of the existing assets. Secondly, the net investment parameter is negative and significant, which implies that the scaled residual income is lower in the first year after an increase in invested capital. Thirdly, the residual income model is significantly more accurate in predicting future residual income due to the inclusion of the scaled net investment variable.

Both results can be compared to the work of Miller and Modigliani (1961). Their assumption that net investments immediately generate residual income into perpetuity should be abandoned, while their conceptual division between residual income from net investments and existing capital is confirmed to be economically and statistically beneficial to the residual income model.

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31 The understanding of the residual income dynamics is essential for the improvement of theory and practice in the field of valuation. This current exploratory research could be extended in a couple of ways.

First, the use of an industry-specific cost of capital ignores company-differences within industries. Firm-level discount rates would improve the accuracy of the residual income calculation. Time-varying variables would also improve the analysis, as it might be interesting to investigate the effects of net investments over time.

Second, the variable ‘net investments’ is chosen to represent a one-year increase in invested capital. However, it might be valuable to assess how residual income is influenced by investments over an extended time period.

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Appendices

A1. Table A1: Overview of industry groups

The table below shows the several activities that are included in each industry group.

Table A1: Overview of industry groups Industry Name

SIC-code

Description of activities

Mining 10 Coal mining, Oil & gas extraction, Mining & quarrying of nonmetallic minerals, except fuels.

Manufacturing - Natural products

20 Food & kindred products, Textile mill products, Apparel & other finished products made from fabrics & similar material, Lumber & wood products, except furniture, Furniture & fixtures; Paper & allied products, Printing, publishing & allied industries.

Manufacturing - Chemical products

28 Chemicals & allied products, Petroleum refining & related industries, Rubber & miscellaneous plastics products, Leather & leather products, Stone, clay, glass & concrete products, Primary metal industries, Fabricated metal products. Manufacturing –

Machinery and equipment

35 Industrial & commercial machinery & computer equipment, Electronic & other electrical equipment & components, except computer equipment, Transportation equipment, Measuring, analyzing & controlling instruments;

photographic, medical & optical goods; watches & clocks, Miscellaneous manufacturing industries.

Transportation, Communications, Electric, Gas and Sanitary service

40 Railroad transportation, Local & suburban transit &

interurban highway passenger transportation, Motor freight transportation & warehousing, Water transportation, Transportation by air, Transportation services, Communications, Electric, gas & sanitary services. Wholesale and retail

trade

50 Wholesale trade-durable goods, Wholesale trade-nondurable goods, Building materials, hardware, garden supply & mobile home dealers, General merchandise stores, Food stores, Automotive dealers & gasoline service stations, Apparel & accessory stores, Home furniture, furnishings & equipment stores, Eating & drinking places, Miscellaneous retail Services 70 Hotels, rooming houses, camps & other lodging places,

Personal services, Business services, Automotive repair, services & parking, Miscellaneous repair services, Motion pictures, Amusement & recreation services, Health services, Legal services, Educational services, Social services,

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33 A2. Table A2: Descriptive statistics of industry-specific variables

Below I present the descriptive statistics of the main variables and the inputs needed to calculate the dependent and independent variables. The mean, median, standard deviation, minimum, maximum and number of observations are presented. For the purpose of readability, the industry names are omitted. SIC-codes correspond to the following industries: SIC-code 10: Mining; 20: Manufacturing – Natural products; 23: Manufacturing – Chemical products; 35: Manufacturing – Machinery and equipment; 40: Transportation, Communications, Electric, Gas and Sanitary service; 50: Wholesale and retail trade; 70: Services. Detailed descriptions of the industry groups can be found in Appendix A1.

Table A2: Descriptive statistics of industry-specific variables

Variable: Current year's residual income (USD) (𝑋𝑖𝑡)

10 $ 331,912.16 $ 24,067.85 $ 3,125,349.40 $ -20,156,262.00 $ 41,071,135.00 1066 20 $ 299,453.67 $ 41,522.90 $ 1,092,407.30 $ -4,881,080.50 $ 10,323,778.00 1620 28 $ 337,477.09 $ 7,445.38 $ 1,496,973.80 $ -12,505,163.00 $ 22,845,329.00 3241 35 $ 149,446.23 $ 10,323.75 $ 1,708,258.00 $ -38,244,426.00 $ 43,508,286.00 5172 40 $ 185,925.34 $ 35,255.50 $ 1,082,437.80 $ -12,703,268.00 $ 16,441,464.00 2622 50 $ 205,331.36 $ 29,285.16 $ 725,106.59 $ -4,036,605.70 $ 9,603,899.00 2702 70 $ 211,817.45 $ 11,707.82 $ 1,621,870.40 $ -41,255,269.00 $ 17,879,792.00 2822 All $ 225,808.41 $ 17,594.28 $ 1,557,695.50 $ -41,255,269.00 $ 43,508,286.00 19245

Variable: Previous year's residual income (USD) (𝑋𝑖𝑡−1)

10 $ 462,021.25 $ 29,339.29 $ 3,013,399.60 $ -9,624,000.50 $ 41,071,135.00 1007 20 $ 286,558.82 $ 39,624.89 $ 1,079,075.20 $ -4,881,080.50 $ 10,323,778.00 1535 28 $ 347,206.45 $ 7,709.77 $ 1,462,726.30 $ -12,505,163.00 $ 22,845,329.00 3058 35 $ 142,462.85 $ 10,396.24 $ 1,599,589.10 $ -38,244,426.00 $ 36,324,982.00 4880 40 $ 172,321.37 $ 34,926.53 $ 1,033,120.90 $ -12,703,268.00 $ 16,441,464.00 2475 50 $ 198,657.78 $ 28,779.14 $ 712,509.98 $ -4,036,605.70 $ 9,603,899.00 2561 70 $ 203,795.19 $ 11,255.15 $ 1,617,291.10 $ -41,255,269.00 $ 17,879,792.00 2659 All $ 227,744.08 $ 17,553.44 $ 1,501,793.20 $ -41,255,269.00 $ 41,071,135.00 18175

Variable: Previous year's net investments (USD) (𝐼𝑖𝑡−1)

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34

Table A2: Descriptive statistics of industry-specific variables, cont’d

Variable: Invested capital (in USD) (𝐴𝑖𝑡)

10 $ 5,673,069.00 $ 1,412,336.00 $ 16,684,917.00 $ -60,466.00 $ 205,800,000.00 1139 20 $ 4,402,474.70 $ 1,043,000.00 $ 8,421,632.80 $ -23,565.00 $ 61,834,000.00 1731 28 $ 3,638,966.20 $ 287,883.00 $ 12,019,919.00 $ -3,188,400.00 $ 181,700,000.00 3567 35 $ 3,692,409.40 $ 356,296.00 $ 23,419,061.00 $ -2,970,000.00 $ 584,700,000.00 5765 40 $ 8,188,562.00 $ 2,644,861.00 $ 16,262,444.00 $ -26,560,000.00 $ 242,700,000.00 2793 50 $ 2,873,852.60 $ 562,375.50 $ 8,754,743.20 $ -1,036,000.00 $ 125,300,000.00 2974 70 $ 2,100,538.90 $ 322,341.00 $ 7,264,727.00 $ -1,788,517.00 $ 174,100,000.00 3221 All $ 4,083,651.20 $ 554,324.00 $ 15,846,667.00 $ -26,560,000.00 $ 584,700,000.00 21190

Variable: Market value of equity (𝑀𝑉𝐸𝑖𝑡)

10 $ 10,996,990.00 $ 2,077,350.00 $ 43,933,583.00 $ 300.00 $ 473,300,000.00 1111 20 $ 8,721,460.00 $ 1,750,580.00 $ 22,695,484.00 $ 1,320.00 $ 184,900,000.00 1676 28 $ 9,746,777.50 $ 797,430.00 $ 29,349,502.00 $ 40.00 $ 282,100,000.00 3391 35 $ 7,743,167.30 $ 1,055,775.00 $ 29,870,995.00 $ 1,060.00 $ 748,300,000.00 5472 40 $ 8,368,645.70 $ 2,337,785.00 $ 19,491,817.00 $ 6,830.00 $ 230,900,000.00 2622 50 $ 7,305,948.10 $ 1,264,440.00 $ 21,841,840.00 $ 150.00 $ 283,200,000.00 2824 70 $ 8,083,785.70 $ 1,081,770.00 $ 31,311,688.00 $ 1,710.00 $ 517,200,000.00 2949 All $ 8,414,588.50 $ 1,240,700.00 $ 28,305,873.00 $ 40.00 $ 748,300,000.00 20045

Variable: Book value of equity (in USD) (𝐵𝑉𝐸𝑖𝑡)

10 $ 4,576,475.40 $ 972,362.00 $ 15,813,745.00 $ -602,616.00 $ 174,400,000.00 1140 20 $ 2,691,946.50 $ 675,952.00 $ 5,641,184.40 $ -13,244,000.00 $ 39,619,000.00 1734 28 $ 2,947,480.00 $ 245,286.00 $ 10,533,643.00 $ -3,141,200.00 $ 155,000,000.00 3585 35 $ 2,230,600.00 $ 394,448.00 $ 7,988,189.70 $ -17,311,000.00 $ 130,600,000.00 5795 40 $ 3,976,976.20 $ 1,042,029.00 $ 9,236,485.50 $ -25,560,000.00 $ 122,700,000.00 2810 50 $ 2,024,472.50 $ 431,059.00 $ 5,780,867.80 $ -1,956,000.00 $ 81,394,000.00 2991 70 $ 2,057,305.00 $ 313,277.50 $ 8,331,717.70 $ -3,590,000.00 $ 152,100,000.00 3252 All $ 2,689,206.20 $ 443,726.00 $ 8,894,115.80 $ -25,560,000.00 $ 174,400,000.00 21307

Variable: Earnings before interest and taxes (in USD) (𝐸𝐵𝐼𝑇𝑖𝑡)

Extending the residual income dynamics of Ohlson (1995): An analysis of the effects of net investments and industries.

Extending the residual income dynamics of Ohlson (1995): An

analysis of the effects of net investments and industries.

Extending the residual income dynamics of Ohlson (1995): An

analysis of the effects of net investments and industries.

Table of contents

1. Introduction

2. Theoretical background and hypothesis development

3. Methodology

4. Results

5. Discussion and conclusion

Appendices